Modelling with Functions What is a mathematical model? A mathematical model simplifies a real-world situation so it can be described using mathematics The model can then be used to make predictions...
Solving Equations Analytically How can I solve equations analytically where the unknown appears only once? How can I solve equations analytically where the unknown appears more than once? Sometimes...
Exponential Functions & Graphs What is an exponential function? What are the key features of exponential graphs? The graphs have a y-intercept at (0, 1) The graphs do not have any roots For a &...
Reciprocal Functions & Graphs What is the reciprocal function? What are the key features of the reciprocal graph? Linear Rational Functions & Graphs What is a rational function? What are th...
Graphing Functions How do I graph the function y = f(x)? What is the difference between “draw” and “sketch”? If asked to sketch you should: Show the general shape Label any key points such as the i...
Composite Functions What is a composite function? How do I find the domain and range of a composite function? Exam Tip Worked Example Inverse Functions What is an inverse function? What are ...
Language of Functions What is a mapping? A mapping transforms one set of values (inputs) into another set of values (outputs) Mappings can be: One-to-one Each input gets mapped to exactly one uniqu...
Discriminants What is the discriminant of a quadratic function? How does the discriminant of a quadratic function affect its graph and roots? Forming equations and inequalities using the discrimina...
Quadratic Inequalities What affects the inequality sign when rearranging a quadratic inequality? The inequality sign is unchanged by... Adding/subtracting a term to both sides Multiplying/dividing ...
